"What does economic evidence tell us about the effects of rent control?"

From the Brookings Institution. Not, the last time I checked, a member of the Vast Right-Wing Conspiracy.

Rent control appears to help affordability in the short run for current tenants, but in the long-run decreases affordability, fuels gentrification, and creates negative externalities on the surrounding neighborhood. These results highlight that forcing landlords to provide insurance to tenants against rent increases can ultimately be counterproductive.